Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 19

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CHAPTE R 14? Entropy and Free Energy

14.5 ? Predicting Spontaneity
Gibbs Free-Energy Change, ????G
According to the second law of thermodynamics, ?Suniv > 0 for a spontaneous process. What we
are usually concerned with and usually measure, however, are the properties of the system rather
than those of the surroundings or those of the universe overall. Therefore, it is convenient to have
a thermodynamic function that enables us to determine whether or not a process is spontaneous by
considering the system alone.
We begin with Equation 14.8. For a spontaneous process,
?Suniv = ?Ssys + ?Ssurr > 0
Substituting –?Hsys/T for ?Ssurr, we write

(?

)

?Hsys
?Suniv = ?Ssys + ? –???_____?? > 0
?
??
?
T
Multiplying both sides of the equation by T gives
T?Suniv = T?Ssys ? ?Hsys > 0
Now we have an equation that expresses the second law of thermodynamics (and predicts whether
or not a process is spontaneous) in terms of only the system. We no longer need to consider the
surroundings. For convenience, we can rearrange the preceding equation, multiply through by –1,
and replace the > sign with a < sign:
–T?Suniv = ?Hsys ? T?Ssys < 0
According to this equation, a process carried out at constant pressure and temperature is spontaneous if the changes in enthalpy and entropy of the system are such that ?Hsys ? T?Ssys is less
than zero.
To express the spontaneity of a process more directly, we introduce another thermodynamic
function called the Gibbs1 free energy (G), or simply free energy.
Equation 14.9

G = H ? TS

Each of the terms in Equation 14.9 pertains to the system. G has units of energy just as H and
TS do. Furthermore, like enthalpy and entropy, free energy is a state function. The change in free
energy, ?G, of a system for a process that occurs at constant temperature is
Equation 14.10

Student Annotation: In this context, free
energy is the energy available to do work.
Thus, if a particular process is accompanied
by a release of usable energy (i.e., if ?G is
negative), this fact alone guarantees that
it is spontaneous, and there is no need to
consider what happens to the rest of the
universe.

?G = ?H ? T?S

Equation 14.10 enables us to predict the spontaneity of a process using the change in enthalpy, the
change in entropy, and the absolute temperature. At constant temperature and pressure, for processes that are spontaneous as written (in the forward direction), ?G is negative. For processes that
are not spontaneous as written but that are spontaneous in the reverse direction, ?G is positive. For
systems at equilibrium, ?G is zero.
• ?G < 0 
The reaction is spontaneous in the forward direction (and nonspontaneous in
the reverse direction).
• ?G > 0 
The reaction is nonspontaneous in the forward direction (and spontaneous in
the reverse direction).
• ?G = 0
The system is at equilibrium.
Often we can predict the sign of ?G for a process if we know the signs of ?H and ?S. Table 14.4
shows how we can use Equation 14.10 to make such predictions.
Based on the information in Table 14.4, you may wonder what constitutes a “low” or a
“high” temperature. For the freezing of water, 0°C is the temperature that divides high from low.
1

Josiah Willard Gibbs (1839–1903), an American physicist, was one of the founders of thermodynamics. Gibbs was a modest and private
individual who spent almost all his professional life at Yale University. Because he published most of his work in obscure journals, Gibbs
never gained the eminence that his contemporary and admirer James Maxwell did. Even today, very few people outside of chemistry and
physics have ever heard of Gibbs.

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